Date: Tuesday, September 22, 2015
Location: Rockefeller Hall 310
Pizza lunch at noon in Rockefeller Hall 305
Title: Integer Distance Problems
Abstract: There are many classic unsolved problems in low-dimensional geometry whose statements are relatively easy to comprehend because they simply ask that certain quantities be integers or rational numbers. For example, a 3-by-4 rectangle is “perfect” because its edge and diagonal lengths are integers; but does a “perfect box” exist, one whose edges, face diagonals, and body diagonals all have integer lengths? For another example, is there a point inside of a unit square that is a rational distance from each of the four corners of the square?
In this talk, I will focus on a problem of Erdős: For what positive integers n do there exist configurations of n points in the plane, no three of these points on a line and no four of these points on a circle, such that all of the distances between pairs of points are integers? Can you find an example configuration with n=4 points? Along the way, I will highlight some recent work with undergraduate students that might provide assistance in the search for these configurations.